Yes they are powered .... XLR from the board. You said pins swapped? Is that something that can happen from the factory the cable was manufactured at? I can give you more info on how I have it all set up but its pretty straight forward. Board outputs (Presonus Studiolive 24.4.2 AI) to bottom subs Ch. 1 ...then short jumper XLR's to Ch. 1 on the tops... But if you want more info I can provide if I know what you need

Yes, factories make mistakes too.

If you have cables, you need to be able to test them. A multimeter (if you do sound, you should have one) will do but a cable tester is faster.

Even rooms can do odd things to phase relationships. With the system in its usual place invert the polarity of one of the subs (or even the input of the whole stack) and listen to what happens. Does the problem get better or worse? This may or not solve the problem, but it might give you a clue. If you can't just invert the polarity at the console or at the speakers themselves, get a A3M to A3F coupler and wire it for reverse polarity.

There certainly could be XLRs wired wrong.You mentioned:"The last two gigs as I walked around the club on my wireless at volume for mid sized club, I have been noticing a weird sucking sensation on my eardrums? It seems that this sucking sensation only happens when our band is playing, not so much during the break music."You likely don't also play your break music through your monitors and stage gear- when you hear the combination of both while walking off stage the difference can be rather stark, and room changes interacting with monitors and mains as you walk around can be huge, regardless of individual speaker polarities.If by "my wireless" you mean in ear monitors, forget about them being "in phase" (or polarity) with the mains as you walk around.